4. If the graph of \( y=-x^{2}+6 x-5 \) is reflected in the \( x \)-axis and the resulting graph is then reflected in the \( y \)-axis, the new equation is (A) \( y=-(x-3)^{2}+4 \) (B) \( y=-x^{2}-6 x-5 \) (C) \( y=(x+3)^{2}+4 \) (D) \( y=x^{2}+6 x+5 \)

To solve the problem, we'll perform the required reflections step by step on the given quadratic equation \( y = -x^2 + 6x - 5 \). **Step 1: Reflect the graph in the \( x \)-axis.** Reflecting a graph over the \( x \)-axis changes the sign of the \( y \)-values. This means we replace \( y \) with \( -y \): \[ -y = -x^2 + 6x - 5 \\ \Rightarrow y = x^2 - 6x + 5 \] **Step 2: Reflect the resulting graph in the \( y \)-axis.** Reflecting a graph over the \( y \)-axis changes the sign of the \( x \)-values. This means we replace \( x \) with \( -x \) in the equation: \[ y = (-x)^2 - 6(-x) + 5 \\ \Rightarrow y = x^2 + 6x + 5 \] The final equation after both reflections is: \[ y = x^2 + 6x + 5 \] **Answer:** (D) \( y=x^{2}+6 x+5 \)